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1. A=sage.combinat.partition.number_of_partitions() is marked for deprecation in favour of B=sage.combinat.partitions.number_of_partitions(), which is what function A() calls most of the time. As agreed above, number_of_partitions() will stay in the global name space, but this made the deprecation somewhat fiddly as I did not want to deprecate number_of_partitions() for "normal use" because from the user perspective this function will not change. Instead, I have deprecated the individual options of number_of_partitions() so deprecation warnings are only generated when A() does NOT call B(). In the global namespace, number_of_partitions still points to A(). When the functions which are marked for deprecation below are removed, number_of_partitions() should be changed to point to B() and A() should be changed into a deprecated_function_alias to B(). See the patch for more details.

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2. For use in Partitions().random_element() the function number_of_partitions() was cached. This cached function was almost never used so, assuming that caching this function is a good idea, I decided to cache sage.combinat.partitions.number_of_partitions() always. Please let me know if this is a bad idea.

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2. For use in Partitions().random_element() the function number_of_partitions() was cached. This cached function was almost never used so, assuming that caching this function is a good idea, I decided to cache sage.combinat.partitions.number_of_partitions() always. Please let me know if this is a bad idea. ''In fact, this leads to a dramatic speed-up. See the timings below''.